I'm really confuzzled as to why this:

foreach my $value ( @$subarray ) {
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would eat up memory.

That line expands the contents of the array into a list (Ie. On Perls' stack). If the subarray pointed by $subarray is large, it will consume a large amount of memory to do that.

You can avoid that by indexing the array, rather than aliasing it's elements. Eg.

for my $index ( 0 .. $#$subarray ) {
    my $value = $subarray->[ $index ];
    ...
}
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Or, if you need to modify the elements, substitue $subarray->[ $index ] wherever you are currently using $value.